I would like to compile the source code for gap on an IBM PC running DOS.

I downloaded the 386 executable a few months ago and haven't had too many
problems with it (actually the only problem I had is using the
"Edit(filename)" command which I could not get to work; but since
Exec("myeditor filename") works fine, that hasn't been much of an abstacle.)
I have also been using the gcc compiler for DOS for a while and would like
to try it out on the gap source code. Is there a "system.c" file for DOS
and do I need anything else to generate the executable myself?

There is a system.dos file included with any sufficiently recent
distribution of the GAP sources. Apart from that and a suitable
makefile (which depends rather heavily on your make file
unfortunately - if I can find mine on-line anywhere (I'm away from
my PC until Christmas) I'll send it directly to you) there's nothing
you need.

I'd recommend avoiding DJGPP 1.06, as I found that programs using
that version of GO32 hung erratically every half-hour or so. Any
later version should work fine, as did 1.05.